Problem: Solve for $x$. Enter the solutions from least to greatest. $6x^2 - 18x - 240 = 0$ $\text{lesser }x = $
Answer: $\begin{aligned} 6x^2 - 18x - 240 &= 0 \\\\ 6(x^2-3x-40)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-3x-40$ can be factored as $(x+5)(x-8)$. $\begin{aligned} 6(x+5)(x-8)&=0 \\\\ x+5=0&\text{ or }x-8=0 \\\\ x=-5&\text{ or }x=8 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -5 \\\\ \text{greater }x &= 8 \end{aligned}$